00:01
So this problem wants us to evaluate the limit as x is approaching negative infinity of 4x minus 3 over the square of 25x squared plus 4x.
00:08
So this is an interesting problem because we can use a tactic that we often use when we have the square root or a cube or any root when we're evaluating limits is to just take the square root of the polynomial with the highest power.
00:23
Because if we visualize this as x is getting smaller and smaller as it's approaching negative infinity, when we square it, we're going to have.
00:30
Have this really, really big number.
00:31
And then we're going to have plus 4x.
00:33
And as x gets bigger and bigger and bigger, this plus 4x becomes more irrelevant.
00:37
Because if we just have that square root of a 25x squared, and then we compare it to the square of 25x squared plus 4x, this plus 4x, once taking a square root and comparing those two numbers, won't make a really big difference when evaluating.
00:50
So if we think about even a bigger number, like 10 million or 100 million, and we plug those numbers in, that plus 4x really makes a very small difference it compares into the x squared term.
01:01
But because we're approaching negative infinity, we have to keep something in mind.
01:05
If we're approaching negative infinity in the numerator, we just get negative infinity because it's going to keep getting smaller and smaller and smaller as the polynomials power is one...